# String confinement in 2-form lattice gauge theory

## TL;DR

This paper investigates how vortex strings are confined in a dual lattice gauge theory of the abelian Higgs model, revealing a phase-dependent linear potential and mapping the phase diagram.

## Contribution

It introduces a study of string confinement in a 2-form lattice gauge theory and derives the phase diagram of the model.

## Key findings

- Linear confining potential in the confinement phase
- Disappearance of confinement in the deconfinement phase
- Phase diagram illustrating different regimes

## Abstract

We study the confinement between vortex strings in the dual lattice gauge theory of the abelian Higgs model. The dual lattice gauge theory is described by a 2-form gauge field. We calculate the string-antistring potential from the surface operator of the 2-form gauge field. The linear confining potential appears in a confinement phase and it disappears in a deconfinement phase. The phase diagram of the theory is also obtained.